Something happened to demoralised Labour MPs while most of them were on the beach this August. They stumbled on an issue that embarrasses David Cameron and generates genuine public support, ranging from old-fashioned letters to the editor to hyperactivity on Twitter and the blogosphere.

Unfortunately for Labour the issue is not as shiny new as Twitter. It is the NHS, that old election standby whenever the party of Aneurin Bevan is in a tight electoral corner. Will it work again next time? Andy Burnham, Gordon Brown's health secretary, hopes so.

None of this was on Downing Street's media grid for August. But the ferocity of the debate now engulfing Barack Obama's plans to reform America's healthcare system – which is brilliant but unfair, expensive and inefficient – has spilled over into Britain for two reasons. Diehard US opponents of Britain's "socialist, fascist" (sic) NHS are using it – and Canada's publicly funded system – to attack Obama. And the publicity-minded Tory MEP Daniel Hannan joined the onslaught.

It was Hannan's description of the NHS as "a 60-year-old mistake" which Americans must avoid at all costs that lit the blue touchpaper on rabid Fox TV. Labour pounced on it, a "welovethenhs" hashtag went viral on Twitter and Cameron was forced to dismiss his pushy young colleague's slapdash views – most of the 1.4 million NHS staff are administrators, claimed Hannan – as "eccentric".

Andrew Lansley, the party's health spokesman, duly popped up to reassure voters for the umpteenth time that the detoxed Cameroon Tories really do embrace the core principles of the NHS: taxpayer-funded and free at the point of use, unless you count dentistry and hospital parking fees. After all, everyone knows how it looked after the Camerons' late son, Ivan.

In reality both parties have compromised in the worldwide search for a fair and affordable healthcare system in an age when non-smoking, fit people live longer but end-of-life care, not to mention hi-tech cures for chronic conditions, cost a lot. As New Labour's leftwing critics on the blogosphere never cease to complain, the party embraced choice and market competition.

Burnham himself is said to be keener to promote the Blairite purchaser/provider split pioneered in the 80s by Ken Clarke than was Alan Johnson. Although he criticised Lansley yesterday for promoting local pay bargaining (would the Tories tackle the GPs' inflated contract as well as Unison?), he too favours local decision-making.

He may not like Lansley's idea for an arm's-length management board to run the NHS either – even Bupa-types have doubts – but has long championed his own version of an NHS constitution. It is not that no policy differences survive (will Lansley really abolish targets such as the 18-week hospital wait, or simply call them something else?), only that they are narrower than for decades.

It may not matter to some voters. What the shrill US debate suggests is that healthcare reform has become part of the ongoing "culture wars" between modernisers and those millions of Americans who don't travel and fear that aliens are taking over their country – with NHS-style "death panels" of bureaucrats who decide who lives and dies.

Such bizarre talk drowns out rational debate, also available on some websites, about the strengths and weaknesses of US, UK, French, German, and Singapore (Hannan's preferred model) healthcare systems: all have their problems. There are echoes of cultural irrationality in the British debate where the NHS is either perfect or a Stalinist monster, Hannan either a traitor or a libertarian hero.

The trend to watch is actually growing convergence and co-operation on health within the EU. Now that poses a real dilemma for a Cameron cabinet.